<p>Exclusive production of a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>χ</mi><mrow><mi>c</mi><mn>1</mn></mrow></msub></math> axial vector quarkonia in photon-proton scattering at high energies requires a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi></math>-odd <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>t</mi></math>-channel exchange. In the limit of vanishing momentum transfer this occurs either via the exchange of a photon, the Primakoff process, where the spin of the proton does not change. For axial-vector meson production, as a consequence of the Landau-Yang theorem, the Primakoff cross section is finite as <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>t</mi><mo stretchy="false">→</mo><mn>0</mn></math>. Alternatively, a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi></math>-odd spin dependent Odderon can be exchanged, which involves a spin flip of the proton. The resulting cross section is related to the square of the collinear trigluon correlator or the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>k</mi><mo>⊥</mo></msub></math>-moment of the gluon Sivers function. Using two models for the gluon Sivers function from the literature we compute the ratio of Sivers to Primakoff cross sections and the angular coefficient <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>λ</mi><mi>θ</mi></msub></math> governing the angular distribution of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>χ</mi><mrow><mi>c</mi><mn>1</mn></mrow></msub><mo stretchy="false">→</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><mo>+</mo><mi>γ</mi></math> decay as functions of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>x</mi></math>. We point out that these observables constrain the magnitude of the gluon Sivers function at small <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>x</mi></math> which could be accessed in electron-proton scattering and ultraperipheral proton-proton and nucleus-proton collisions.</p>

Croatia

Sanjin Benić

United States

Adrian Dumitru

Poland

Leszek Motyka

Tomasz Stebel

Gluon Sivers function from forward exclusive <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>χ</mi></mrow><mrow><mi>c</mi><mn>1</mn></mrow></msub></mrow></math> photoproduction on unpolarized protons

Exclusive <math><mi>C</mi><mo>=</mo><mo>+</mo><mn>1</mn></math> scalar, axial-vector, and tensor quarkonium production in high-energy electron-proton scattering requires a <math><mi>C</mi></math>-odd <math><mi>t</mi></math>-channel exchange of a photon or a three-gluon ladder. We derive the expressions for the corresponding amplitudes. The relative phase of the photon vs three-gluon exchange amplitudes is determined by the sign of the light-front matrix element of the eikonal color current operator <math><msup><mi>d</mi><mrow><mi>a</mi><mi>b</mi><mi>c</mi></mrow></msup><msup><mi>J</mi><mrow><mo>+</mo><mi>a</mi></mrow></msup><msup><mi>J</mi><mrow><mo>+</mo><mi>b</mi></mrow></msup><msup><mi>J</mi><mrow><mo>+</mo><mi>c</mi></mrow></msup></math> at moderate <math><mi>x</mi></math>, and is not affected by small-<math><mi>x</mi></math> QCD evolution. Model calculations predict constructive interference, which is particularly strong for momentum transfer <math><mrow><mo>|</mo><mi>t</mi><mo>|</mo><mo>∼</mo><mn>1</mn><mtext> </mtext><mtext> </mtext><msup><mrow><mi>GeV</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></math> where the cross section for <math><msub><mi>χ</mi><mrow><mi>c</mi><mi>J</mi></mrow></msub></math> production exceeds that for pure photon exchange by up to a factor of 4. Exclusive <math><msub><mi>χ</mi><mrow><mi>c</mi><mi>J</mi></mrow></msub></math> electroproduction at the high luminosity Electron-Ion Collider occurs with well measurable rates and measurements of these processes should find evidence for the perturbative odderon exchange. We also compute the total electroproduction cross section as a function of energy and provide first estimates of the number of <math><msub><mi>χ</mi><mrow><mi>c</mi><mi>J</mi></mrow></msub></math> events per month at the Electron-Ion Collider design luminosity.

Abhiram Kaushik

Photon-odderon interference in exclusive <math><mrow><msub><mrow><mi>χ</mi></mrow><mrow><mi>c</mi></mrow></msub></mrow></math> charmonium production at the Electron-Ion Collider

We compute the back-to-back dijet cross section in deep inelastic scattering at small <math><mi>x</mi></math> to next-to-leading order (NLO) in the color glass condensate effective field theory. Our result can be factorized into a convolution of the Weizsäcker-Williams gluon transverse-momentum-dependent distribution function (WW gluon TMD) with a universal soft factor and an NLO coefficient function. The soft factor includes both double and single logarithms in the ratio of the relative transverse momentum <math><mrow><msub><mrow><mi>P</mi></mrow><mrow><mo>⊥</mo></mrow></msub></mrow></math> of the dijet pair to the dijet momentum imbalance <math><msub><mi>q</mi><mo>⊥</mo></msub></math>; its renormalization group (RG) evolution is resummed into the Sudakov factor. Likewise, the WW TMD obeys a nonlinear RG equation in <math><mi>x</mi></math> that is kinematically constrained to satisfy both the lifetime and rapidity ordering of the projectile. Exact analytical expressions are obtained for the NLO coefficient function of transversely and longitudinally polarized photons. Our results allow for the first quantitative separation of the dynamics of Sudakov suppression from that of gluon saturation. They can be extended to other final states and provide a framework for precision tests of novel QCD many-body dynamics at the Electron-Ion Collider.

France

Paul Caucal

Farid Salazar

Björn Schenke

Raju Venugopalan

Back-to-Back Inclusive Dijets in Deep Inelastic Scattering at Small <math><mi>x</mi></math>: Complete NLO Results and Predictions

In [1], we performed the first complete computation of the back-to-back inclusive dijet cross-section in Deeply Inelastic Scattering (DIS) at small x Bj to next-to-leading order (NLO) in the Color Glass Condensate effective field theory (CGC EFT). We demonstrate here that for dijets with relative transverse momentum P ⊥ and transverse momentum imbalance q ⊥, to leading power in q ⊥/P ⊥, the cross-section for longitudinally polarized photons can be fully factorized into the product of a perturbative impact factor and the non-perturbative Weizsäcker-Williams (WW) transverse momentum dependent (TMD) gluon distribution to NLO accuracy. The impact factor can further be expressed as the product of a universal soft factor which resums Sudakov double and single logs in P ⊥/q ⊥ and a coefficient function given by a remarkably compact analytic expression. We show that in the CGC EFT the WW TMD satisfies a kinematically constrained JIMWLK renormalization group evolution in rapidity. This factorization formula is valid to all orders in Q  s /q ⊥ for q ⊥, Q  s  ≪ P ⊥, where Q  s  is the semi-hard saturation scale that grows with rapidity.

Back-to-back inclusive dijets in DIS at small x: gluon Weizsäcker-Williams distribution at NLO

The quarkonium production mechanism in high-multiplicity small collision systems has recently been pursued in the color-glass-condensate (CGC) effective theory combined with the nonrelativistic QCD (NRQCD) factorization, allowing us to study initial state interactions. Quarkonium polarization, potentially measured in future experiments, would help elucidate the quarkonium production mechanism at high multiplicities. In this paper, we provide predictions on <math><mrow><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow></math> polarization parameters in high-multiplicity proton-proton (<math><mi>p</mi><mi>p</mi></math>) and proton-nucleus (<math><mi>p</mi><mi>A</mi></math>) collisions within the <math><mrow><mi>CGC</mi><mo>+</mo><mi>NRQCD</mi></mrow></math> framework. Theoretical predictions are given for <math><mi>J</mi><mo>/</mo><mi>ψ</mi></math> rapidity <math><mn>2.5</mn><mo>&lt;</mo><msub><mi>y</mi><mrow><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow></msub><mo>&lt;</mo><mn>4</mn></math>, charged-particle multiplicity pseudorapidity <math><mrow><mo>|</mo><msub><mrow><mi>η</mi></mrow><mrow><mi>ch</mi></mrow></msub><mo>|</mo><mo>&lt;</mo><mn>1</mn></mrow></math>, and energies <math><msqrt><mi>S</mi></msqrt><mo>=</mo><mn>13</mn><mtext> </mtext><mtext> </mtext><mi>TeV</mi></math> for <math><mi>p</mi><mi>p</mi></math> collisions and <math><msqrt><mi>S</mi></msqrt><mo>=</mo><mn>8.16</mn><mtext> </mtext><mtext> </mtext><mi>TeV</mi></math> for <math><mi>p</mi><mi>A</mi></math> collisions. Considering two leptonic frame choices (the Collins-Soper and helicity frames) we find a weak polarization of <math><mi>J</mi><mo>/</mo><mi>ψ</mi></math> that additionally decreases with growing event activities. No significant system size dependence between <math><mi>p</mi><mi>p</mi></math> and <math><mi>p</mi><mi>A</mi></math> collisions is obtained—this could be a new constraint to initial state interactions in small collision systems.

Kazuhiro Watanabe

<math><mi>J</mi><mo>/</mo><mi>ψ</mi></math> polarization in high multiplicity <math><mi>p</mi><mi>p</mi></math> and <math><mi>p</mi><mi>A</mi></math> collisions: <math><mrow><mi>CGC</mi><mtext> </mtext><mo>+</mo><mtext> </mtext><mi>NRQCD</mi></mrow></math> approach

We study the prompt photon hadroproduction at the LHC with the <math><msub><mi>k</mi><mi>T</mi></msub></math>-factorization approach and the <math><mi>q</mi><msup><mi>g</mi><mo>*</mo></msup><mo>→</mo><mi>q</mi><mi>γ</mi></math> and <math><mrow><msup><mrow><mi>g</mi></mrow><mrow><mo>*</mo></mrow></msup><msup><mrow><mi>g</mi></mrow><mrow><mo>*</mo></mrow></msup><mo>→</mo><mi>q</mi><mover><mrow><mi>q</mi></mrow><mrow><mo>¯</mo></mrow></mover><mi>γ</mi></mrow></math> partonic channels, using three unintegrated gluon distributions which depend on gluon transverse momentum. They represent three different theoretical schemes which are usually considered in the <math><msub><mi>k</mi><mi>T</mi></msub></math>-factorization approach, known under the acronyms: KMR, CCFM, and GBW gluon distributions. We find sensitivity of the calculated prompt photon transverse momentum distribution to the gluon transverse momentum distribution. The predictions obtained with the three approaches are compared to data, that allows to differentiate between them. We also discuss the significance of the two partonic channels, confronted with the expectations which are based on the applicability of the <math><msub><mi>k</mi><mi>T</mi></msub></math>-factorization scheme in the high energy approximation.

Krzysztof Golec-Biernat

Prompt photon production in proton collisions as a probe of parton scattering in high energy limit

We discuss the Drell–Yan dilepton production using the transverse momentum dependent parton distributions evolved with the Catani–Ciafaloni–Fiorani–Marchesini–Kwieciński (CCFM-K) equations in the single loop approximation. Such equations are obtained assuming angular ordering of emitted partons (coherence) for $$x\sim 1$$ <math><mrow><mi>x</mi><mo>∼</mo><mn>1</mn></mrow></math>  and transverse momentum ordering for $$x \ll 1$$ <math><mrow><mi>x</mi><mo>≪</mo><mn>1</mn></mrow></math> . This evolution scheme also contains the Collins–Soper–Sterman (CSS) soft gluon resummation. We make a comparison with a broad class of data on transverse momentum spectra of low mass Drell–Yan dileptons.

Drell–Yan production with the CCFM-K evolution

We present theoretical predictions for selected differential cross sections for the process $$pp \rightarrow t {\bar{t}}B$$ <math><mrow><mi>p</mi><mi>p</mi><mo>→</mo><mi>t</mi><mover><mrow><mi>t</mi></mrow><mrow><mo>¯</mo></mrow></mover><mi>B</mi></mrow></math>  at the LHC, where B can be a Higgs (H), a Z or a W boson. The predictions are calculated in the direct QCD framework up to the next-to-next-leading logarithmi accuracy and matched to the complete NLO results including QCD and electroweak effects. Additionally, results for the total cross sections are provided. The calculations deliver a significant improvement of the theoretical predictions, especially for the $$ t {\bar{t}}H$$ <math><mrow><mi>t</mi><mover><mrow><mi>t</mi></mrow><mrow><mo>¯</mo></mrow></mover><mi>H</mi></mrow></math>  and the $$ t {\bar{t}}Z$$ <math><mrow><mi>t</mi><mover><mrow><mi>t</mi></mrow><mrow><mo>¯</mo></mrow></mover><mi>Z</mi></mrow></math>  production. In these cases, predictions for both the total and differential cross sections are remarkably stable with respect to the central scale choice and carry a substantially reduced scale uncertainty in comparison with the complete NLO predictions.

Germany

Anna Kulesza

Daniel Schwartländer

Vincent Theeuwes

Associated top quark pair production with a heavy boson: differential cross sections at NLO + NNLL accuracy

Color charge correlations in the proton at moderately small <math><mi>x</mi><mo>∼</mo><mn>0.1</mn></math> are extracted from its light-cone wave function. The charge fluctuations are far from Gaussian and they exhibit interesting dependence on the impact parameter and on the relative transverse momentum (or distance) of the gluon probes. We provide initial conditions for small-<math><mi>x</mi></math> Balitsky-Kovchegov evolution of the dipole scattering amplitude with impact parameter and <math><mover><mi>r</mi><mo>^</mo></mover><mo>·</mo><mover><mi>b</mi><mo>^</mo></mover></math> dependence, and with a nonzero <math><mi>C</mi></math>-odd component due to three-gluon exchange. Lastly, we compute the (forward) Weizsäcker-Williams gluon distributions, including the distribution of linearly polarized gluons, up to fourth order in <math><msup><mi>A</mi><mo>+</mo></msup></math>. The correction due to the quartic correlator provides a transverse momentum scale, <math><mrow><mrow><mi>q</mi><mo>≳</mo><mn>0.5</mn></mrow><mtext> </mtext><mtext> </mtext><mi>GeV</mi></mrow></math>, for nearly maximal polarization.

Vladimir Skokov

Subfemtometer scale color charge correlations in the proton

We propose a new process which probes the BFKL dynamics in the high energy proton-proton scattering, namely the forward Drell-Yan (DY) production accompanied by a backward jet, separated from the DY lepton pair by a large rapidity interval. The proposed process probes higher rapidity differences and smaller transverse momenta than in the Mueller-Navelet jet production. It also offers a possibility of measuring new observables like lepton angular distribution coefficients in the DY lepton pair plus jet production.